Derivatives of spectral aerosol optical depth for partitioning type and loading

ABSTRACT

A spectral method is provided for partitioning type and loading with aerosol optical depth. Based on multi-spectral optical aerosol depth, particle-size distribution and refractive index are derived by normalizing first- and second-order derivatives for processing quantitative calibration of main components. According to the optical feature parameters of various aerosol types, a radiation theory is applied to simulate multi-spectral optical depth for each density, including those of mixed types. The intrinsic parameters of aerosol types are figured out by constructing normalized derivative aerosol indices (NDAI). The clear characteristic differences between aerosol types are used to figure out main components of aerosols and their mixing ratios. The simulation result of the normalized index of various aerosol type is in good agreement with the ground observation data of Aerosol Robotic Network. It shows that NDAI is quite practicable in quantitative calibration of main components of atmospheric aerosol.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to partitioning aerosol type and loading;more particularly, to using normalized derivative aerosol index (NDAI)to integrate data of theoretical simulation and actual observation forexamining various aerosol types with the relationships of particle-sizedistributions and complex refractive indices together with first- andsecond-order derivatives of spectral aerosol optical depths (AOD), whereoptical intrinsic parameters of dust (DS), biomass burning (BB), andanthropogenic pollutants (AP) are constructed; and, thus, each singleaerosol type is identified and main components of each mixed aerosol arequantitatively distinguished.

DESCRIPTION OF THE RELATED ARTS

According to the reports of the Intergovernmental Panel on ClimateChange, since various aerosol types have different optical features, thevariation range of global atmospheric aerosol radiative forcing isobviously larger than the average value following the changes in timeand space; and it has a great influence on the accuracy in the radiativeforcing assessment of aerosol. It also shows that various aerosol types,such as black carbon, the main component of BB, and sulfate and nitrate,the main components of AP, do not have equal influences on radiativeforcing. Therefore, how to effectively distinguish various types ofatmospheric aerosols and their contents is very important.

Satellite observation has the advantage of periodicity and wide range.If it can be applied to global or regional aerosol observation, it ishelpful for the accurate assessment of aerosol radiative forcing. Forassisting satellite in the inversion of aerosol parameters, the globalAErosol RObotic NETwork (AERONET) provides inspections of variousaerosol parameters in the atmosphere. At the same time, it is confirmedthat the optical features of aerosols, such as spectral changes onparticle-size distribution, single-scattering albedo (SSA), etc.,obtained by observation for a long time can be used to identify aerosoltypes. But for the mixed aerosol types, a single type of parameterthreshold does not meet the requirements for identification.

Previous research by Kaku et al. showed that not only multi-spectraloptical parameters provide particle-size distribution, but alsoscattering and extinction coefficients are calculated theoretically bythe spectral deconvolution algorithm (DSA+). Hansell et al. appliedfirst- and second-order derivatives of high-spectral optical depth tosuccessfully distinguish BB aerosol and cirrus clouds as showing thehigh correlation of their main components (types) to the spectralchanges of AODs. The above are quite feasible for identifying anddistinguishing aerosol types.

As a result, owing to the shortcomings in conventional technologies,there is an urgent need for improving the existing deficiencies byeffectively constructing a set of optical intrinsic parameters of DS,BB, and AP for identifying each single aerosol type as well asquantitatively distinguishing main components of each mixed aerosol.Hence, the prior arts do not fulfill all users' requests on actual use.

SUMMARY OF THE INVENTION

The main purpose of the present invention is to apply first- andsecond-order derivatives obtained through multi-spectral AODnormalization for identifying and quantitatively distinguishing aerosoltypes.

Another purpose of the present invention is to obtain the potential ofsatellite application on providing global or regional distribution ofaerosol type.

Another purpose of the present invention is to provide information ofthe temporal and spatial distribution of SSA having very scarce globalobservation data.

To achieve the above purposes, the present invention is a method ofspectral AOD derivatives for partitioning type and loading, comprisingsteps of: (a) first step: based on optical feature parameters of variousaerosol types, using a model of Second Simulation of a Satellite Signalin the Solar Spectrum (6S model) to calculate spectral AODs of thevarious aerosol types, where the various aerosol types comprises DS, BB,AP, and various mixtures of DS, BB, and AP; and (b) second step: basedon the spectral AODs of the various aerosol types, processingcalculation with NDAIs to obtain particle-size distributions and complexrefractive indices derived from normalized first- and second-orderderivatives of the spectral AODs of the various aerosol types to obtainintrinsic parameters of the various aerosol types to calculate maincomponents of aerosols and mixing ratios thereof to identify each singletype of aerosol and quantitatively distinguish main components of mixedaerosol.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood from the followingdetailed description of the preferred embodiment according to thepresent invention, taken in conjunction with the accompanying drawings,in which

FIG. 1 is the view showing the preferred embodiment according to thepresent invention;

FIG. 2 is the view showing the spectral distributions of the spectralaerosol optical depths (AOD);

FIG. 3A is the view showing the first-order derivatives of theunnormalized AODs;

FIG. 3B is the view showing the first-order derivatives of thenormalized AODs;

FIG. 3C is the view showing the second-order derivatives of theunnormalized AODs;

FIG. 3D is the view showing the second-order derivatives of thenormalized AODs;

FIG. 4A is the view showing the unnormalized first-order parameters;

FIG. 4B is the view showing the normalized first-order parameters;

FIG. 4C is the view showing the unnormalized second-order parameters;

FIG. 4D is the view showing the normalized second-order parameters;

FIG. 4E is the view showing the unnormalized second-order derivatives ofthe AOD intrinsic features;

FIG. 4F is the view showing the normalized second-order derivatives ofthe AOD intrinsic features;

FIG. 5 is the view showing the result integrating theoretical simulationand actual observation;

FIG. 6 is the view showing the result integrating theoretical simulationand actual observation by using the normalized aerosol indices;

FIG. 7 is the view showing the normalized first- and second-orderderivatives of the data of ground observation and theoreticalsimulation; and

FIG. 8A and FIG. 8B are the views showing the component proportions ofthe three representative aerosols.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The following description of the preferred embodiment is provided tounderstand the features and the structures of the present invention.

Please refer to FIG. 1 to FIG. 8B, which are a view showing a preferredembodiment according to the present invention; a view showing spectraldistributions of AODs; a view showing first-order derivatives ofunnormalized AODs; a view showing first-order derivatives of normalizedAODs; a view showing second-order derivatives of unnormalized AODs; aview showing second-order derivative of normalized AODs; a view showingunnormalized first-order parameters; a view showing normalizedfirst-order parameters; a view showing unnormalized second-orderparameters; a view showing normalized second-order parameters; a viewshowing unnormalized second-order derivatives of AOD intrinsic features;a view showing normalized second-order derivatives of AOD intrinsicfeatures; a view showing a result integrating theoretical simulation andactual observation; a view showing a result integrating theoreticalsimulation and actual observation by normalized aerosol indices; a viewshowing normalized first- and second-order derivatives of data of groundobservation and theoretical simulation; and a view showing componentproportions of three representative aerosols. As shown in the figures,the present invention is a method of spectral AOD derivatives forpartitioning type and loading, where a normalized derivative aerosolindex (NDAI) is used to integrate data of theoretical simulation andactual observation for examining various aerosol types with therelationships of particle-size distributions and complex refractiveindices together with first- and second-order derivatives of spectralAODs and constructing optical intrinsic parameters of dust (DS), biomassburning (BB), and anthropogenic pollutants (AP); and, thus, each singletype of aerosol is identified and main components of each mixed aerosolare quantitatively distinguished. The present invention comprises thefollowing steps:

(a) Processing theoretical simulation s1: Regarding a theoreticalsimulation, based on optical feature parameters of various aerosoltypes, a model of Second Simulation of a Satellite Signal in the SolarSpectrum (6S model) is used to calculate spectral aerosol optical depths(AOD) of the various aerosol types. The various aerosol types comprisesDS, BB, AP, and various mixtures of DS, BB, and AP, where the maincomponent of BB is black carbon and the main components of AP aresulfate and nitrate. Therein, the optical feature parameters of thevarious aerosol types are based on particle-size distributions andcomplex refractive indices of aerosols provided by the WorldMeteorological Organization (WMO). As listed in Table 1, n_(r) and n_(i)are the real number part and the imaginary number part of the complexrefractive index, respectively; R_(mean) is a geometric mean radius; andR_(std) is a geometric standard deviation.

TABLE 1 λ DS AP BB (micrometer, μm) n_(r) n_(i) n_(r) n_(i) n_(r) n_(i)0.400 1.53 8.00E−03 1.53 5.00E−03 1.75 0.46 0.488 1.53 8.00E−03 1.535.00E−03 1.75 0.45 0.515 1.53 8.00E−03 1.53 5.00E−03 1.75 0.45 0.5501.53 8.00E−03 1.53 6.00E−03 1.75 0.44 0.633 1.53 8.00E−03 1.53 6.00E−031.75 0.43 0.694 1.53 8.00E−03 1.53 7.00E−03 1.75 0.43 0.860 1.528.00E−03 1.52 1.20E−02 1.75 0.43 1.536 1.4 8.00E−03 1.51 2.30E−02 1.770.46 2.250 1.22 9.00E−03 1.42 1.00E−02 1.81 0.50 3.750 1.27 1.10E−021.452 4.00E−03 1.90 0.57 R_(mean) (μm) 0.50 0.005 0.0118 R_(std) (σ)2.99 2.99 2.00

(b) Obtaining spectral AOD derivatives s2: Based on the spectral AODs ofthe various aerosol types, NDAIs are used for calculation to deriveparticle-size distributions and complex refractive indices from first-and second-order derivatives of the spectral AODs of the various aerosoltypes for examination and to construct intrinsic parameters of thevarious aerosol types for calculating main components of aerosols andmixing ratios thereof.

According to traditional formula, a first-order derivative of spectralAOD of gap between λ₁ and λ₂ is figured out as shown in Eq.(1), whichreflects the particle-size distribution as covering the influence of AODyet unable to single out particle size information. For removing theinfluence of AOD, the present invention improves the first-orderderivative, as shown in Eq.(2), which is defined as a normalized aerosolindex. With the building of the normalized aerosol index, the affect ofAOD on the particle-size distribution is greatly reduced, where theparticle-size distributions of the DS, BB (black carbon), and AP(sulfate and nitrate) are clearly distinguished.

$\begin{matrix}{{\frac{\partial\tau}{\partial\lambda} \approx {\nabla\tau_{({\lambda_{1},\lambda_{2}})}}} = {\frac{\tau_{\lambda_{1}} - \tau_{\lambda_{2}}}{\Delta\lambda} = {\tau_{\lambda_{2}} \times \left( {1 - A^{\alpha}} \right) \times B}}} & (1)\end{matrix}$ $\begin{matrix}{{{NDAI}_{({\lambda_{1},\lambda_{2}})} \equiv {{\nabla\tau_{({\lambda_{1},\lambda_{2}})}}/\tau_{\lambda_{ref}}}},} & (2)\end{matrix}$

where Δλ=λ₂−λ₁, A=λ₂/λ₁ and B=1/(λ₂−λ₁) are constants of specific bands;λ is a wavelength (μm); α is an Ångstrom exponent (AE, related toparticle-size distribution); ∇τ_((λ) ₁ _(,λ) ₂ ₎ is a first-orderderivative of spectral AOD of gap between λ₁ and λ₂; τ_(λ) _(ref) is anormalization reference of various AOD size; and NDAI_((λ) ₁ _(,λ) ₂ ₎is a spectral derivative of gap between λ₁ and λ₂ as being normalizedwith τ_(λ) _(ref) .

The second-order derivative of AOD spectrum (as shown in Eq.(3)) isrelated to the imaginary number part of the refractive index. Afterbeing normalized (as shown in Eq.4)), features of and differencesbetween the various aerosol types on scattering and absorption aredescribed to distinguish and identify the various aerosol types.

$\begin{matrix}{{\frac{\partial^{2}\tau}{\partial\lambda^{2}} \cong {\nabla^{2}\tau_{({\lambda_{1},\lambda_{2},\lambda_{3}})}}} = \frac{\left( {\tau_{\lambda_{1}} - {2\tau_{\lambda_{2}}} + \tau_{\lambda_{3}}} \right)}{\left( {\lambda_{1} - \lambda_{2}} \right)\left( {\lambda_{2} - \lambda_{3}} \right)}} & (3)\end{matrix}$ $\begin{matrix}{{{{\frac{\partial^{2}\tau}{\partial\lambda^{2}}/\tau_{\lambda_{ref}}} \cong {{\nabla^{2}\tau_{({\lambda_{1},\lambda_{2},\lambda_{3}})}}/\tau_{\lambda_{ref}}}} = \frac{\left( {\tau_{\lambda_{1}} - {2\tau_{\lambda_{2}}} + \tau_{\lambda_{3}}} \right)/\tau_{\lambda_{ref}}}{\left( {\lambda_{1} - \lambda_{2}} \right)\left( {\lambda_{2} - \lambda_{3}} \right)}},} & (4)\end{matrix}$

where τ_(λ) _(ref) is selected from τ_(λ) ₁ , τ_(λ) ₂ , and τ_(λ) ₃ tobind a dynamic range to the spectral derivative of a various aerosoltype.

For distinguishing AODs in a mixed aerosol of two main componentscomprising A-type component and B-type component, the change of AODdepends on the AOD fraction (fAOD) for each type. As shown in Eq.(5),Δτ_((λ) ₁ _(,λ) ₂ ₎ ^(ABmixed) =f _(AOD) ^(A)Δτ_((λ) ₁ _(,λ) ₂ ₎ ^(A) +f_(AOD) ^(B)Δτ_((λ) ₁ _(,λ) ₂ ₎ ^(B)  (5),

where f_(AOD) ^(A) and f_(AOD) ^(B) are the fAOD(NDAI) in the spectrum(λ₁,λ₂) of the mixed aerosol comprising the A-type component and B-typecomponent; and f_(AOD) ^(A)+f_(AOD) ^(B)=1. Based on Eq.(2), Eq.(5)further derives Eq.(6) based on the normalized aerosol index.NDAI_((λ) ₁ _(,λ) ₂ ₎ ^(ABmixed)=∇τ_((λ) ₁ _(,λ) ₂ ₎ ^(ABmixed)/τ_(ref)=f _(AOD) ^(A)NDAI_((λ) ₁ _(,λ) ₂ ₎ ^(A) +f _(AOD) ^(B)NDAI_((λ) ₁ _(,λ)₂ ₎ ^(B)  (6)

Eq.(6) is the theoretical basis for calculating the fraction ratios ofthe main components in the mixed aerosol based on the normalized aerosolindex. With the coordination of the optical intrinsic parameters of thevarious aerosol types built with the normalized aerosol indices,specific ratios of the various aerosol types are obtained as shown inEq.(7).

$\begin{matrix}{{{f_{AOD}^{A} = \frac{{NDAI}_{({\lambda_{1},\lambda_{2}})}^{{mean} - A} - {NDAI}_{({\lambda_{1},\lambda_{2}})}^{ABmixed}}{{NDAI}_{({\lambda_{1},\lambda_{2}})}^{{mean} - A} - {NDAI}_{({\lambda_{1},\lambda_{2}})}^{{mean} - B}}};{f_{AOD}^{B} = {1 - f_{AOD}^{A}}}},} & (7)\end{matrix}$

where NDAI_((λ) ₁ _(,λ) ₂ ₎ ^(mean-A) and NDAI_((λ) ₁ _(,λ) ₂ ₎^(mean-B) are intrinsic parameters of A-type aerosol and B-type aerosol;and NDAI_((λ) ₁ _(,λ) ₂ ₎ ^(ABmixed) is an intrinsic parameter of A/Bmixed-type aerosol. Thus, a novel method of spectral AOD derivatives forpartitioning type and loading is obtained.

The following states-of-use are only examples to understand the detailsand contents of the present invention, but not to limit the scope ofpatent of the present invention.

For actual measurement, the main observation data are the spectral AODdata obtained through long-term observation of the Aerosol RoboticNetwork (AERONET) observation stations distributed globally, whichcomprises main source areas of DS, BB (black carbon) and AP (sulfate andnitrate). As shown in Table 2, the control data set and verificationdata set obtained from the AERONET are used to identify aerosol type.

TABLE 2 Control data set (used to construct NDAI) AP DS BB August-April-May March-May September Beijing Chiang Mai Beijing (39 N, 116 E)(18 N, 98 E)  (39 N, 116 E) 2001-2012 2006-2012 2001-2012 DalanzadgadMukdahan Hong Kong (43 N, 104 E) (16 N, 104 E) (22 N, 114 E) 1997-20122003-2010 2005-2012 Solar Village Pimai Taihu (24 N, 46 E)  (15 N, 102E) (31 N, 120 E) 1998-2012 2003-2008 2005-2012 Tamanrasset Taipei (22 N,5 E)   (25 N, 121 E) 2006-2012 2002-2012 Validation data set (used toevaluate NDAI) AP DS BB August- April-May March-May September(2014-2016) (2014-2016) (2014-2016) Beijing Chiang Mai Beijing (39 N,116 E) (18 N, 98 E)  (39 N, 116 E) La Laguna Doi Ang Khang Durban UKZN(28 N, 16 W)  (19 N, 99 E)  (30 S, 31 E)  XuZhou Luang Namtha Hong Kong(34 N, 117 E) (20 N, 101 E) (22 N, 114 E) Zinder Airport Maeson LaLaguna (14 N, 9 E)   (19 N, 99 E)  (28 N, 16 W)  Mongu Inn Mongu Inn (15S, 23 E)  (15 S, 23 E)  NhaTrang Taihu (12 N, 109 E) (31 N, 120E) OmkoiTaipei (17 N, 98 E)  (25 N, 121 E) Silpakorn Univ XuZhou (13 N, 100 E)(34 N, 117 E) Ubon Ratchathani (15 N, 104 E) Vientiane (17 N, 102 E)[Experiment Result and Analysis]Theoretical Spectral AOD Derivatives

The spectral distributions of different AODs at specific wavelengths(0.44 μm, 0.47 μm, 0.55 μm, 0.66 μm, 0.675 μm, 0.87 μm, and 1.02 μm) aresimulated based on the 6S experimental data set using various aerosols(i.e. Table 1); and a Bezier curve method is used in FIG. 2 to connectdiscrete points. The circular data points in the figure are the spectrumdistributions of DS aerosol, which shows a flat trend with a smallincrease in wavelength; and the square data points and triangular datapoints are the spectral distributions of AP and BB aerosols,respectively, which tends to decrease continuously as similar totraditional research results. As AE indices show, the spectral gradientis mainly related to particle-size information, which shows that theradius of DS aerosol is much larger than the radius of AP and BBaerosols. Although similar particle sizes may increase the difficulty ofdistinguishing AP from BB, their spectral gradients are still slightlydifferent. Besides, it is worth noting that, even for the same type, thespectral gradient of AOD may also vary with the optical depth(AOD_((0.55 μm))=0.4, 0.8, 1.2, 1.6 and 2.0).

As shown in FIG. 2 , it may be difficult to distinguish AP and BBaerosols in the zero-order spectrums by simply simulating the detailedchanges in the spectral AODs. However, spectral derivative can promotethe identification of subtle changes in AODs caused by differentscattering and absorption. Hence, spectral derivative is related toparticle-size distribution and complex refractive index for enhancingaerosol intrinsic feature. Based on the data shown in FIG. 2 , FIG. 3Adescribes first-order derivatives of AODs and ∇τ_((λ) ₁ _(,λ) ₂ ₎, whichare the spectrum pairs of 0.44-0.55 μm, 0.55-0.675 μm, 0.675-0.87 μm,and 0.87-1.02 μm from DS, AP, and BB aerosols, respectively. Differentcurves with the same shape of data points represent AOD_((0.55 μm))values of 0.4, 0.8, 1.2, 1.6, and 2.0, respectively. The values of DSaerosol become almost flat along wavelengths (i.e., they all tend to bezero). Obviously, except DS (due to the flat distribution of spectralAODs), the difference of ∇τ_((λ) ₁ _(,λ) ₂ ₎ between AP and BB aerosolsbecomes more obvious in the shorter wavelength spectrums following AODchanges and deviates. For the second-order derivatives of AOD beforenormalization, each of the three groups of DS, AP, and BB aerosols hasthree continuous spectral AODs (0.44-0.55-0.675 μm, 0.55-0.675-0.87 μm,and 0.675-0.87-1.02 μm) as shown in FIG. 3C. Although the differencebetween AP and BB aerosols can be further magnified in terms of ∇²τ, thevalue of the second-order derivative still depends on AOD size, which issimilar to ∇τ_((λ) ₁ _(,λ) ₂ ₎ as shown in FIG. 3A. On acquiringintrinsic features, both the first- and second-order derivatives areimportant for normalization as shown in FIG. 3B and FIG. 3D. Afternormalization using AOD_((0.44 μm)), each type of curve under differentAOD begins to merge into its own intrinsic spectrum. The opticalintrinsic parameters of DS, AP, and BB aerosols effectively eliminateAOD effect.

According to the above simulation results, the first- and second-orderderivatives of the unnormalized AODs are still affected by AOD size.But, as shown in FIG. 3A and FIG. 3C, a closely-overlapped line isobtained after normalization; and the intrinsic parameters of theparticle-size distributions and scattering/absorption of variousaerosols are clearly shown in FIG. 3B and FIG. 3D.

When different types of aerosols are mixed, the optical features areusually diverse. Thus, the first- and second-order derivatives are usedto discuss the dynamic range caused by the mixing effect of DS, AP, andBB aerosols. As shown in FIG. 4A to FIG. 4F., the pre- andpost-normalized first- and second-order derivatives (FIG. 4A and FIG. 4Cvs. FIG. 4B and FIG. 4D) are compared for AOD (τ_(0.44 μm)) based on thespectral AODs at 0.44 μm, 0.675 μm, and 0.87 μm. In the figures, thetriangle-symbolized BB, the square-symbolized AP, and thecircle-symbolized DS aerosols have their area positions proved by thefirst- and second-order derivatives before and after normalization (FIG.4E and FIG. 4F). Therein, the dotted lines between the symbols representthe dynamic ranges of mixed DS-AP, DS-BB and AP-BB aerosols.

As shown in the results, FIG. 4B, FIG. 4D, and FIG. 4F show that thenormalized first- and second-order derivatives do not change asfollowing the changes in AODs, which highlights the importance of thenormalization in acquiring intrinsic parameters of particle-sizedistribution and scattering/absorption. The measurement of spectral AODderivatives is shown exactly as the first derivatives of the spectralAODs (∇_((0.44,0.675))), where both 6S-model simulation (shown indiagram (a) of FIG. 5 ) and the AERONET measurement (shown in diagram(b) of FIG. 5 ) reveal the changes of particle size (α) and AOD (τ).Furthermore, the slope of each aerosol type in the theoreticalsimulation is more consistent with the in-situ measurement, whichstrongly supports the NDAI method proposed in the present invention.

Based on the data set used in diagram (b) of FIG. 5 , FIG. 6 processesthe filtration of AOD_((0.44 μm))>0.8 under Single Scattering Albedo(SSA) and normalizes the result through AOD_((0.87 μm)). Besides, themapping (dashed line) for normal distribution and the average value(black dot) are also indicated.

In the above results shown in the figures, the result of the first-orderderivatives (particle-size distribution) of the ground observation data(AERONET) before and after normalization (FIG. 5 v.s. FIG. 6 ) stronglysupports the result of the theoretical simulation (shown in FIG. 4A-FIG.4F), where various aerosol types can be clearly distinguished (shown inFIG. 6 ).

FIG. 7 shows that the second-order derivatives (normalized ∇2τ) andfirst-order derivatives (normalized ∇τ) of two-component aerosolmixtures (DS-BB, DS-AP, and AP-BB, denoted with “6S”) are obtained toprocess simulation through the mixed volume/density weights for the 6Smodel in 0.01 steps from 0.00 to 1.00. The ground observation data(AERONET) and the average value and standard deviation of the spectralderivatives of DS, AP, BB, DS-AP, DS-BB, and AP-BB aerosols areconfigured together.

FIG. 7 shows the comparison between the first- and second-orderderivatives of the data of the ground observation (AERONET) and thetheoretical simulation, where a good consistency is shown in the figureand the normalized first- and second-order derivatives of the spectralAODs constructed by the present invention have considerable feasibilityand application value in identifying and quantifying aerosol types.

Regarding practical applications, the present invention often applies toa variety of mixed aerosols, where the component proportions of threeglobal representative aerosols are constructed through theory,comprising DS, BB (black carbon), and AP (sulfate and nitrate), forpractical observation applications. As with the result shown in FIG. 8Aand FIG. 8B, the first-order derivative (VT) is the optical features ofparticle-size distribution at 0.44 μm and 0.675 μm calculated for themixed weights of volume and density in 0.01 steps from 0.00 to 1.00. Incontrast, the second-order derivatives (∇²τ) are the calculated opticalfeatures related to refractive indices at 0.44 μm, 0.675 μm, and 0.87μm. It means that, with the mixed volume/density weights of thethree-component mixtures (i.e. mixture of DS, AP, and, BB aerosols) inthe 6S model, the normalized second-order derivatives (∇²τ, related torefractive index at 0.44 μm, 0.675 μm, and 0.87 μm) of AOD_((0.47 μm))is used to process simulation for the first-order derivatives (VT,related to particle-size distribution at 0.44 μm and 0.675 μm) in 0.01steps from 0.00 to 1.00. In this way, with the calculated first-order(X-axis) and second-order (Y-axis) derivatives of the spectral AODs,corresponding aerosol types and their proportions can be found accordingto the database of FIG. 8A and FIG. 8 .B.

It is still a challenge to quantify the compositions of aerosols(atmospheric particulate matter) with the data obtained from satellitetelemetry or ground observation. Based on multi-spectral AODs,particle-size distributions and refractive indices are derived bynormalizing first- and second-order derivatives for processingquantitative calibration of main components. At first, according to theoptical feature parameters of various aerosol types (DS, BB, and AP), aradiation theory (6S model) is applied to simulate the multi-spectraloptical depth for each density, including those of mixed types. Theintrinsic parameters of the aerosol types are figured out with thenormalized derivative aerosol index (NDAI) constructed according to thepresent invention. The apparent differences between the features ofaerosols are used to figure out the main components of any specificaerosol and its mixing ratio. A simulation result of the NDAIs of thevarious aerosol types derived through applying the theory proposed inthe present invention is in good agreement with the ground observationdata of AERONET. It shows that the NDAI constructed according to thepresent invention is quite practicable in the quantitative calibrationof the main components of atmospheric aerosols.

Hence, the main contributions of the present invention are as follows:

1. First- and second-order derivatives obtained through multi-spectralAOD normalization is applied for identifying and quantitativelydistinguishing aerosol types.

2. The potential of satellite applications is obtained for providingglobal or regional distributions of aerosol types.

3. Information of the temporal and spatial distribution of SSA havingvery scarce global observation data can be provided.

To sum up, the present invention is a method of spectral AOD derivativesfor partitioning type and loading, where NDAI is used to integrate dataof theoretical simulation and actual observation for examining variousaerosol types with the relationships of particle-size distributions andcomplex refractive indices together with first- and second-orderderivatives of spectral AODs and constructing optical intrinsicparameters of DS, BB, and AP; and, thus, each single type of aerosol isidentified and main components of each mixed aerosol are quantitativelydistinguished.

The preferred embodiment herein disclosed is not intended tounnecessarily limit the scope of the invention. Therefore, simplemodifications or variations belonging to the equivalent of the scope ofthe claims and the instructions disclosed herein for a patent are allwithin the scope of the present invention.

What is claimed is:
 1. A method of calculating spectral derivatives ofaerosol optical depth (AOD) comprising: measuring optical featureparameters of various mixed aerosol types including dust (DS), biomassburning (BB), anthropogenic pollutants (AP), and mixtures of DS, BB, andAP; determining a Second Simulation of a Satellite Signal in the SolarSpectrum (6S) model by calculating spectral AODs of said various mixedaerosol types; calculating normalized derivative aerosol indices (NDAI)based on the spectral AODs, thereby obtaining particle-sizedistributions and complex refractive indices derived from normalizedfirst- and second-order derivatives of said spectral AODs of saidvarious mixed aerosol types and intrinsic parameters of said variousmixed aerosol types; and calculating main components of the mixedaerosols and mixing ratios thereof identifying each single type ofaerosol and quantitatively distinguishing main components of the mixedaerosols.
 2. The method according to claim 1, wherein a main componentof said BB is black carbon and main components of said AP are sulfateand nitrate.
 3. The method according to claim 1, wherein said opticalfeature parameters of said various mixed aerosol types are measuredparticle-size distributions and complex refractive indices provided bythe World Meteorological Organization (WMO).
 4. The method according toclaim 1, wherein, with the normalization of said first-order derivativesof said spectral AODs of said various aerosol types, said particle-sizedistributions of DS, BB, and AP are clearly distinguished by an equationas follows:NDAI_((λ) ₁ _(,λ) ₂ ₎≡∇τ_((λ) ₁ _(,λ) ₂ ₎/τ_(λ) _(ref) , wherein λ is awavelength (micrometer, μm); ∇τ_((λ) ₁ _(,λ) ₂ ₎ is a first-orderderivative of spectral AOD of gap between λ₁ and λ₂; τ_(λ) _(ref) is anormalization reference of loading of spectral AOD; and NDAI_((λ) ₁_(,λ) ₂ ₎ is a spectral derivative of gap between λ₁ and λ₂ as beingnormalized with τ_(λ) _(ref) .
 5. The method according to claim 1,wherein, normalizing the second-order derivatives of said spectral AODsof said various mixed aerosol types, distinguishes and identifiesfeatures of and differences between said various mixed aerosol types[[on]] with respect to scattering and absorption by an equation asfollows:${{{\frac{\partial^{2}\tau}{\partial\lambda^{2}}/\tau_{\lambda_{ref}}} \cong {{\nabla^{2}\tau_{({\lambda_{1},\lambda_{2},\lambda_{3}})}}/\tau_{\lambda_{ref}}}} = \frac{\left( {\tau_{\lambda_{1}} - {2\tau_{\lambda_{2}}} + \tau_{\lambda_{3}}} \right)/\tau_{\lambda_{ref}}}{\left( {\lambda_{1} - \lambda_{2}} \right)\left( {\lambda_{2} - \lambda_{3}} \right)}},$wherein τ_(λ) _(ref) is a normalization reference of loading of spectralAOD and is selected from τ_(λ) ₁ , τ_(λ) ₂ , and τ_(λ) ₃ to bind adynamic range to spectral derivative of said various aerosol type; and λis a wavelength.